Explain why Social Security Number is considered a qualitative variable even though it contains numbers.

Being numbers doesnt mean that the variable is quantitative. Those numbers need to have some meaning other than a mere identification.

There should be a relation on elements with similar numbers and the number ordering should mean something: if i have a higher number of centimeters than you, then i am taller, otherwise i am smaller. If a i have 4 pencils and you have 8, then you have the double amount of pencils than me.

In the case of social security number there is no meaning on having a greater number other than being a different number, there is no meaning if, for example, my number is twice as big as yours. The only importance of this numbers is to identify the people, they could have used letters instead, thats why it is a qualitative variable instead of a quantitative one.